Pathwise superhedging for time-dependent barrier options on càdlàg paths—Finite or infinite tradeable European,One-Touch,lookback or forward starting options

We establish pathwise duality using simple predictable trading strategies for the robust hedging problem associated with a barrier option whose payoff depends on the terminal level and the infimum of a càdlàg strictly positive stock price process, given tradeable European options at all strikes at a single maturity. The result allows for a significant dimension reduction in the computation of the superhedging cost, via an alternate lower-dimensional formulation of the primal problem as a convex optimization problem, which is qualitatively similar to the duality which was formally sketched using linear programming arguments in Duembgen and Rogers [10] for the case where we only consider continuous sample paths. The proof exploits a simplification of a classical result by Rogers (1993) which characterizes the attainable joint laws for the supremum and the drawdown of a uniformly integrable martingale (not necessarily continuous), combined with classical convex duality results from Rockefellar (1974) using paired spaces with compatible locally convex topologies and the Hahn–Banach theorem. We later adapt this result to include additional tradeable One-Touch options using the Kertz and Rösler (1990) condition. We also compute the superhedging cost when in the more realistic situation where there is only finite tradeable European options; for this case we obtain the full duality in the sense of quantile hedging as in Soner (2015), where the superhedge works with probability $1?\epsilon$ where $\epsilon$ can be arbitrarily small), and we obtain an upper bound for the true pathwise superhedging cost. In Section 5, we extend our analysis to include time-dependent barrier options using martingale coupling arguments, where we now have tradeable European options at both maturities at all strikes and tradeable forward starting options at all strikes. This set up is designed to approximate the more realistic situation where we have a finite number of tradeable Europeans at both maturities plus a finite number of tradeable forward starting options.¹     

基于连续模型的人员疏散仿真分析

行人流连续模型直观地反映人群疏散过程中的疏散特征，本文基于行人流连续模型。研究行人在典型疏散场景下的疏散特征．在COMSOL中建立行人流连续模型及其方程，通过编写MATLAB代码，实现了连续模型及其循环求解框架．利用快速扫描法求解Eikonal方程得到背景场值，在每一步迭代循环中将背景场值作为模型的初始变量导入，调用COMSOL计算模块求解模型的瞬态控制方程．通过两个标准算例，重现了典型的行人流自组织现象，验证了连续模型的合理性．结果表明，本文的疏散仿真分析模型和计算程序是可靠的，疏散仿真分析可以为实际工程中的人员疏散方案的制定以及平面设计与安全布置等方面提供技术支撑．     

等热流密度加热垂直下降液膜的研究

利用等热流密度加热条件下降膜流动的三维模型方程进行线性稳定性分析和数值模拟。线性稳定性分析表明，模型方程在小到中等Reynolds数下都适用，并且流向不稳定性增长率随着Reynolds数和Marangoni数增加而增加，展向不稳定性增长率则随着Marangoni数增加而增加，随着Reynolds数增加而减小，流向和展向对扰动波数都存在一个不稳定区间。三维数值模拟表明，在等热流密度加热条件下，液膜在随机扰动的情况下最终会形成带孤立波的三维溪流状结构，液膜与气体的换热也因溪流状结构的出现而加强；在随机扰动的基础上引入占优势地位的展向最不稳定扰动会使得换热增强，液膜会提前破裂；在随机扰动的基础上引入占优势地位的流向最不稳定扰动时，液膜的换热会增强，但不会提前破裂；在随机扰动的基础上同时引入占优势地位的流向和展向最不稳定扰动时，换热会加强且液膜会提前破裂。     

1stOpt软件在蔗糖水解实验教学中的应用

将1stOpt软件用于物理化学实验蔗糖水解反应速率常数的测定中，在无需严格记录反应开始时间和测定反应终了旋光度的情况下，通过非线性拟合无需编程及公式变换就可以简单方便准确地得到反应速率常数，避免了传统数据处理方法所带来的人为误差，可以补充和改进物理化学实验的教学。     

每课一题教学环节的研究与实践

利用“每课一题”这个教学环节从已有知识中提取基本原理，并应用于新知识的学习；提取学生的问题编制习题，让学生暴露产生问题的根源并从根本上解决。探讨了每课一题的必要性及其基本类型。     

Effect of deprotonation on the magnetic exchange coupling constant of fluorene‐based verdazyl diradical: A computational study

The magnetic behavior of the fluorene bridged verdazyl diradicals has been studied theoretically in their neutral and deprotonated states. The deprotonation of C9‐H site of the fluorene ring opens a new coupling pathway, which changes the nature of magnetic coupling. The transmission spectra analysis reveals that the transmission through fluorine has also increased due to the opening of a new coupling path after deprotonation.     

Corrigendum on ‘investigation on molecular interaction studies of binary mixture of Dehpa and Petrofin at 298.15 K’

Expressions of Redlich–Kister (RK) excess function using polynomials on difference of molar composition are used. Calculated values of excess properties from experimental values are well presented in some curves as a function of mole fraction (x₂) of the second pure component of the studied binary liquid mixture. Nevertheless, the authors presented values of adjustable parameters, not for the polynomial of the popular RK equation (i.e. vs. x₂–x₁), but for globally the excess property Y^E as an overall three degree polynomial on (x₂) including implicitly the molar fraction product (x₁·x₂) in their nonlinear regression, which can then induces some readers to probable confusion.     

针对连续变化法测定络合物稳定常数实验中可能出现的设计缺陷的讨论

连续变化法测定络合物组成和稳定常数是大学化学中的经典学生实验。但针对1：2和1：3的络合反应，实验教科书的设计中可能出现数据点过少也就是溶液配制过少的问题。如果按照要求配制溶液，由于没有完全反应的混合溶液，而其他混合溶液给出的数据又都呈良好的线性，就缺少了用来估算曲线的数据点，结果是，将没有足够的数据对稳定常数进行估算。对这种可能出现的数据点过少的实验设计的原因、结果和解决方法进行了探讨。     

Influence of cell and LC parameters on the dynamics of STN liquid crystal displays

The dynamics of super-twisted nematic (STN) liquid crystal displays have rarely been studied. In this article, the dynamic response of STN is analysed in detail. The evolution of director configuration with time was obtained by solving Ericksen–Leslie hydrodynamic equations. The time varying midlayer tilt angle is presented as a measure of dynamic response. The influence on STN dynamics of cell parameters including pretilt angle, twist angle, cell thickness, and of material parameters including d/p, K ₂₂, K ₃₃, were studied.